This case study is focused on the impact of big data in exploration and production of oil & gas in the Norwegian Continental Shelf. Overall, the industry is currently transitioning from mere data collection practices to more proactive uses of data, especially in the operations area. Positive economical impacts associated with the use of big data comprise data generation and data analytics business models, commercial partnerships around data, and the embracement of open data by the Norwegian regulator. On the negative side there are concerns regarding the future of existing business models and the reluctance of oil companies to share data. Positive social and ethical impacts include mitigation of safety and environment concerns with big data, personal privacy not really a problem, and creation of new jobs for data scientists; on the other hand cyberthreats are becoming a serious concern and there are trust issues with data.

With the emergence of the Web of Data, there is a need of tools for searching and exploring the growing amount of semantic data. Unfortunately, such tools are scarce and typically require knowledge of SPARQL/RDF. We propose here PepeSearch, a portable tool for searching semantic datasets devised for mainstream users. PepeSearch offers a multi-class search form automatically constructed from a SPARQL endpoint. We have tested PepeSearch with 15 participants searching a Linked Open Data version of the Norwegian Register of Business Enterprises for non-trivial challenges. Retrieval performance was encouragingly high and usability ratings were also very positive, thus suggesting that PepeSearch is effective for searching semantic datasets by mainstream users. We also assessed its portability by configuring PepeSearch to query other SPARQL endpoints.

The variable splitting method for free-variable tableau calculi provides an admissibility condition under which the same free variables can be assigned values independently on different branches. While this has a large potential for automated proof search, a direct implementation of this condition is impractical. We adapt the incremental closure framework for free variables to variable splitting tableaux by recasting the admissibility condition for closing substitutions into a constraint satisfaction problem. The resulting mechanism allows to check the existence of an admissible closing substitution incrementally during the construction of a proof. We specify a rule-based algorithm for testing satisfiability of constraints that accounts for split variables, and present experimental results based on a prototype variable splitting theorem prover implementation measuring the computational overhead of the variable splitting framework.

The paper introduces a free variable, labelled proof system for intuitionistic propositional logic with variable splitting. In this system proofs can be found without backtracking over rules by generating a single, uniform derivation. We prove soundness, introduce a construction that extracts finite countermodels from unprovable sequents, and formulate a branchwise termination condition. This is the first proof system for intuitionistic propositional logic that admits goal-directed search procedures without compromising proof lengths, compared to corresponding tableau calculi.

A new logic of belief (in the "only knowing" family) with confidence levels is presented. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. The explicit form can be found by applying a set of equivalence preserving rewriting rules to the implicit form. The rewriting process is performed entirely within the logic, on the object level, provided we supply an explicit formalization of the logical space. We prove that the problem of deciding whether there exists a consistent explicit form is -complete, a complexity class to which many problems of nonmonotonic reasoning belong. The article also contains a conceptual analysis of basic notions like belief, co-belief and degrees of confidence.

We present a method for trust scenarios with more than one trustee, where sets of trustees are ordered in a relation of relative trustworthiness. We show how a priority structure implicit in a trust relation can be made fully explicit by means of a lattice and how a system of default expectations arises from a systematic interpretation. The default structure lends itself to formal interpretation, but is independent of a particular logical language. The theory is designed to directly extend the analysis of the concept of trust given by Andrew Jones.

We present a framework for reasoning about trustworthiness, with application to conflict resolution and belief formation at various degrees of reliability. On the basis of an assignment of relative trustworthiness to sets of information sources, a lattice of degrees of trustworthiness is constrructed; from this, a priority structure is derived and applied to the problem of forming the right opinion in the presence of possibly conflicting information. Consolidated with an unquestioned knowledge base, this provides an unambiguous account of what an agent should believe, conditionally on which information sources are trusted. Applications in multi-agent doxastic logic are sketched.

We present a weak multi-agent system of Only knowing and an analysis of the logical spaces that can be defined in it. The logic complements the approach to generalizing Levesque's All I Know system made by Halpern and Lakemeyer. A novel feature of our approach is that the logic is defined entirely at the object level with no reference to meta-concepts in the definition of the axiom system. We show that the logic of Halpern and Lakemeyer can be encoded in our system in the form of a particular logical space.

We prove consistency of a sequent calculus for classical logic with explicit splitting of free variables by means of a semantical soundness argument. The free variable system is a mature formulation of the system proposed at TABLEAUX 2003. We also identify some challenging and interesting open research problems.

We prove consistency of a sequent calculus for classical logic with explicit splitting of free variables by means of a semantical soundness argument. The free variable system is a mature formulation of the system proposed at TABLEAUX 2003 [1]. We also identify some challenging and interesting open research problems.

The main construction in this paper is an encoding of default logic into an ``only knowing'' logic with degrees of confidence. By imposing simple and natural constraints on the encoding we show that the ``only knowing'' logic can accommodate ordered default theories and that the constrained encoding implements a prescriptive interpretation of preference between defaults. An advantage of the encoding is that it provides a transparent formal rendition of such a semantics. A feature of the construction is that the generation of extensions can be carried out within the ``only knowing'' logic, using object level concepts alone.

Various multi-modal systems are proposed for the representation of belief states in a multi-agent context. We introduce sequent calculi for these systems and prove cut-elimination results. A corollary to these results is that a new and natural multi-modal extension of Levesque's system of only knowing is consistent.

This paper presents a Kripke semantics for a multi-agent generalization of Levesque's logic of ``only knowing''. We prove soundness and completeness and show that the logic has the finite model property. In addition we prove a Modal reduction theorem which states that complex syntactical representations can be syntactically reduced to a provably equivalent form which directly reflects all the models of the representation.

We provide an interpretation of Kierkegaard's "Philosophical fragments" based on an analysis of the debate between Mynster and Martensen about rationalism and supernaturalism. We argue that the composition of the Fragments in an essential way reflects the manner in which the theological questions under debate were formulated. From this perspective, the Fragments may at first sight seem to bring ample support to Mynster, both in form and in substance. However, we argue that this impression changes radically upon closer examination. Quite to the contrary, we argue that Climacus reformulates the points put forth by Mynster in a way which goes against Mynster's own theological system.

Abstract: A system with variable splitting is introduced for a sequent calculus with free variables and run-time Skolemization. Derivations in the system are invariant under permutation, so that the order in which rules are applied has no effect on the leaves. Technically this is achieved by means of a simple indexing system for formulae, variables and Skolem functions. Moreover, the way in which variables are split enables us to restrict the term universe branchwise.

The article addresses the use of connection methods within non--classical proof systems. It contains an original presentation of the main ideas in the field and the following new results: (1) a clarification of the relationship between the sequent calculus with free variables, free variable tableaux and the matrix system for classical logic. I have in particular identified a new class of sequent calculus skeletons which corresponds to matrices, (2) a new soundness proof for the free variable systems for classical logic based on permutation. The technique is then applied to the nonclassical systems, (3) a sequent calculus rendition of the matrix system for intuitionistic and normal modal logics up to S4 with new proofs of soundness and completeness, (4) new proof systems for modal logics K45 and S5 with quantifiers.

The direct use of connection methods within non-classical proof systems has been limited to matrix characterizations. A main objective for this work has been to present the idea underlying the matrix systems in a simpler way, and in a way which also acc ommodates the related activity within the tableau community. The article contains an original presentation of the main ideas in the field and contains the following new results: (1) a clarification of the relationship between the sequent calculus with f ree variables, free variable tableaux and the matrix system for classical logic. I have in particular identified a new class of sequent calculus skeletons which corresponds to matrices, (2) a new soundness proof for the free variable systems for classic al logic based on permutation. The technique is then applied to the nonclassical systems, (3) a sequent calculus rendition of the matrix system for intuitionistic and normal modal logics up to S4 with new proofs of soundness and completeness, (4) new pr oof systems for modal logics K45 and S5 with quantifiers

We present a framework for reasoning about information sources, with application to conflict resolution and belief formation at various degrees of reliability. On the basis of an assignment of relative trustworthiness to sets of information sources, a lattice of degrees of trustworthiness is constructed; from this, a priority structure is derived and applied to the problem of forming the right opinion. Consolidated with an unquestioned knowledge base, this provides an unambiguous account of what an agent should believe, conditionally on which information sources are trusted. Applications in multi-agent doxastic logic are sketched.

We present a new approach to the logic of \emph{at most}, introducing the notion of \emph{parametric propositions} to modal natural deduction proofs. We apply the method with a natural deduction formulation of the doxastic logic \natded, a new system in the ``only knowing'' family. Using parametric proof rules, we give introduction and elimination rules for belief \emph{at most} that directly match the natural second-order formulation of the concept. \natded is sound and complete with respect to the class of intended models. We conjecture that it weakly normalizes and that it satisfies the subformula property.

We present a weak multi-agent language of Only knowing and an analysis of the logical spaces that can be defined in it. The logic complements the approach to generalizing Levesque`s All I Know system made by Halpern and Lakemeyer. A novel feature of our approach is that the logic is defined entirely at the object level with no reference to meta-concepts in the definition of the axiom system. We show that the logic of Halpern and Lakemeyer can be encoded in our system in the form of a particular logical space.

A new logic of belief (in the "Only knowing" family) withconfidence levels is presented. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. The explicit form can be found by applying a set ofequivalence preserving rewriting rules to the implicit form. The rewriting process is performed entirely within thelogic, on the object level. We prove that the problem of deciding whether there exists a consistent explicit form is

Various multi-modal systems are proposed for the representation of belief states in a multi-agent context. We introduce sequent calculi for these systems and prove cut-elimination results. A corollary to these results is that a new and naturalmulti-modal extension of Levesque's system of only knowing is consistent.

First, a new logic of belief is briefly presented and applied to the analysis of default inference. The logic allows a natural distinction between explicit and implicit belief representations, where the explicit form directly expresses its models. A novelty of the system is that the appeal to coherence intrinsic to the nature of defaults can be accommodated entirely within the object language. We will see that an implicit representation of a given set of defaults, in combination with situation-specific beliefs, can be reduced to a provably equivalent explicit form, and furthermore, that applying an order of precedence to a set of defaults can make such reduction possible where non-ordered defaults do not yield explicit results.